1. The problem is to find the value of $\sin 10^\circ$. 2. Since $10^\circ$ is not one of the standard angles with simple sine values, we can use the sine addition formula or approximate. 3. Using the sine addition formula: $\sin(10^\circ) = \sin(30^\circ - 20^\circ) = \sin 30^\circ \cos 20^\circ - \cos 30^\circ \sin 20^\circ$. 4. Substitute known values: $\sin 30^\circ = \frac{1}{2}$, $\cos 30^\circ = \frac{\sqrt{3}}{2}$. 5. So, $\sin 10^\circ = \frac{1}{2} \cos 20^\circ - \frac{\sqrt{3}}{2} \sin 20^\circ$. 6. Using approximate values: $\cos 20^\circ \approx 0.9397$, $\sin 20^\circ \approx 0.3420$. 7. Calculate: $\sin 10^\circ \approx \frac{1}{2} \times 0.9397 - \frac{\sqrt{3}}{2} \times 0.3420 = 0.46985 - 0.2962 = 0.17365$. 8. Therefore, $\sin 10^\circ \approx 0.1736$ (rounded to 4 decimal places).